Delayed control of a Moore-Greitzer axial compressor model

Several feedback control laws have appeared in the literature concerning th e stabilization of the nonlinear Moore-Greitzer axial compression model. Mo tivated by magnitude and rate limitations imposed by the physical implement ation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotovic. They showed the pot ential benefit of implementing the S-controller through a first-order lag: while the location of the dosed-loop equilibrium achieved with the static c ontrol law was sensitive to poorly known parameters, the dynamic implementa tion resulted in a small limit cycle at a very desirable location, insensit ive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay, This can be seen as an extension of the model with a first-order lag. The delay can either be a r esult of system constraints or be deliberately implemented to achieve bette r system behavior. The resulting closed-loop system is a set of parameter-d ependent delay differential equations. Numerical bifurcation analysis is us ed to study this model and investigate whether the positive results obtaine d for the first-order model persist, even for larger values of the delay.